## Defining parameters

 Level: $$N$$ = $$729 = 3^{6}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$39366$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(729))$$.

Total New Old
Modular forms 660 330 330
Cusp forms 12 6 6
Eisenstein series 648 324 324

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

 $$6 q + O(q^{10})$$ $$6 q + 3 q^{19} - 6 q^{28} + 3 q^{37} - 3 q^{64} - 6 q^{73} - 3 q^{91} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(729))$$

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
729.1.b $$\chi_{729}(728, \cdot)$$ None 0 1
729.1.d $$\chi_{729}(242, \cdot)$$ None 0 2
729.1.f $$\chi_{729}(80, \cdot)$$ 729.1.f.a 6 6
729.1.h $$\chi_{729}(26, \cdot)$$ None 0 18
729.1.j $$\chi_{729}(8, \cdot)$$ None 0 54
729.1.l $$\chi_{729}(2, \cdot)$$ None 0 162

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(729))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(729)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(243))$$$$^{\oplus 2}$$